26 - Substitution with x = atan(theta)

So, what happens when we have instead, , instead of ?

Well, we can do pretty much the same, but substituting for

But why does this work?

Try the substitution.

Let's make sense of this new substitution.

Whew! That was easy!

Don't be overwhelmed by how complicated integrals may seem. These substitutions are meant to be used.

Know these two core substitution techniques, along with the usual integration by parts, u-sub, partial fraction expansion, and YOU WILL BE UNSTOPPABLE.

Ready to practice?

27 - Practice integration via trigonometric substitutions

Interactive Graph